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3 years ago

Where are the minimum and maximum values for f(x) = -2 + 4 cos x on the interval (0,21]?

Mathematics

2 answers:

Dafna11 [192]3 years ago

4 0

Answer:

Step-by-step explanation:

Maximum value is when cos x = 1

So it is -2 + 4(1) = 2.

Minimum value, when cos x = -1:

= -2 + 4(-1) = -6.

Alex_Xolod [135]3 years ago

4 0

Answer:

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Step-by-step explanation:

So let's first look at cos(x) on interval (0,21].

How many rotations is that? Does it at least contain 1 full rotation? If it contains one full rotation that means all the values from -1 to 1 (inclusive) are tagged? If it doesn't contain a full rotation, we might have to dig a little deeper.

So we know x=0 isn't included and that's when cosine is first 1,but this doesn't mean 1 won't be hit later.

Let's figure out the number of rotations:

21/(2pi)=3.3 approximately

This means we make at least 3 rotations.

So this means we definitely will have all the values from -1 to 1 tagged (inclusive).

Now let's look at whole function.

f(x) = -2 + 4 cos x

-2+(-4) to -2+4 will be the range of the function

So the minimum is -6 and the maximum is 2.

So the min occurs when cos(x)=-1 and the max occurs when cos(x)=1.

We have a little over three rotations and remember we can't include x=0.

cos(x)=1

when x=2pi (one full rotation)

when x=4pi (two full rotations)

when x=6pi (three full rotations)

We will stop here because cosine won't be 1 again until a fourth full rotation

cos(x)=-1

when x=pi (half rotation)

When x=3pi (one + half rotation)

When x=5pi (two+half rotation)

We can't include x=7pi (three+half rotation)

because this one is actually not in the interval because 3.5 is more than 3.3 .

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

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Re write the statement 19+7 divided by 2-5 by including one pair of brackets to make the total equal to 8

Oksanka [162]

Answer:

The solution is given below:

Step-by-step explanation:

The computation is shown below:

= 19 + 7 divided by 2 - 5

= (19 + 7) ÷ (2) - 5

= 26 ÷ 2 - 5

= 13 - 5

= 8

Hence, after solving this the value would be 8

Therefore it is equal to the 8

Hence, the given statement is true

6 0

2 years ago

Colin has a pad with x pieces of paper on it. For his first class, he wrote on 5 fewer than half of the pieces of paper in the p

PIT_PIT [208]

Answer:

Colin has 8 sheets left for his third class.

Step-by-step explanation:

Given that:

Total Number of pieces of papers = $x$

Number of pieces of papers used for 1st class = 5 fewer than half of the pieces in the pad

Writing the equation:

$\text{Number of pieces of papers used for 1st class =} \dfrac{x}{2} -5 ...... (1)$

Also, Given that number of pieces of papers used for the 2nd class are 2 more than that of papers used in the 1st class.

$\text{Number of pieces of papers used for 2nd class =} \dfrac{x}{2} -5+2 = \dfrac{x}2 -3 ...... (2)$

Now, number of pieces of papers left for the third class = Total number of pieces of papers in the pad - Number of pieces of papers used in the first class - Number of pieces of papers used in the first class

$\text{number of pieces of papers left for the third class = }x-(\dfrac{x}{2}-5)-(\dfrac{x}{2}-3)\\\Rightarrow x-\dfrac{x}2-\dfrac{x}2+5+3\\\Rightarrow x-x+5+3\\\Rightarrow 8$

So, the answer is:

Colin has 8 sheets left for his third class.

5 0

3 years ago

WILL MARK YOU BRAINLIEST !!!!

liq [111]

Answer:

$\overline {PM} \cong \overline {ON}$ because they are opposite sides of a parallelogram.

Step-by-step explanation:

First of all, let us have a look at the definition of a parallelogram.

A parallelogram is a closed 4 sided figure (i.e. a quadrilateral) made up with two pairs of straight lines such that the two pairs are parallel and equal to each other.

For example, let us consider a quadrilateral ABCD as attached in the diagram in answer area.

The two pair of lines are:

AB, DC and BC, AD

For ABCD to be a parallelogram, the lines

AB and DC must be parallel to each other and AB = DC

AND

BC and AD must be parallel to each other and BC = DA

------------------------------

In the given question, we are given that the quadrilateral MNOP is a parallelogram.

The two pairs opposite lines are OP, NM and PM, ON.

As per the definition of a parallelogram,

OP and NM must be parallel and equal to each other.

AND

PM and ON must be parallel and equal to each other.

$\therefore$ $\overline {PM} \cong \overline {ON}$ .

Hence proved.

6 0

3 years ago

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laila [671]

Answer:

The answer to your question would be C) y = 3x + 2.

Step-by-step explanation:

The components of a slope intercept form equation is the slope and the intercept. The y-intercept is the term thats by itself which, is +2. This means that the line goes through positive 2 on the plane. For the slope, it is always the coefficient thats next to the x variable. In this case, its 3, meaning that the next point that the line will be on is every 3 steps up and 3 steps towards the right. Hope this helps!

7 0

3 years ago

The graphs of f(x) and g(x) are shown below:

Elodia [21]

Answer:

-3.8, 3

Step-by-step explanation:

The solution to a system is where the graph cross each other. If you look to where they intersect to the left of the origin, where x is negative, it appears that they intersect ALMOST at -4, but not quite. So -3.8 is going to have to do since we don't have the equations of either graph to find the exact values of x. To the right of the origin, where x is positive, the graphs cross where x = 3..

8 0

3 years ago

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